Can you explain to me why it is पीती here, instead of पीते? Does this mean the person you talk to is a woman/girl? Because तुम takes te plural, right?
Yes, तुम can be conjugated with पीता or पीती, depending on the person whom you're talking with.
Could someone please explain to me the meaning between हो, हूँ, है, and हैं? thanks guys :-)
It's a bit like the difference between 'am', 'is' and 'are' in English.
हूँ - this means 'am'. मैं हूँ - I am
है - this means 'is'. वह है - he/she is
हैं - this means 'are'. वे हैं - they are.
The complication is with the fact that Hindi has three different words for 'you'.
The most informal, e.g. when speaking to a child: तू है - you are
Casual e.g. when speaking to a friend तुम हो - you are
Formal e.g. when speaking to a stranger or your boss आप हैं - you are.
You just have to learn which different word goes with which pronoun.
Those are the conjugations of होना
मैं हूँ = I am
तू है = You are (informal)
तुम हो = You are (plural/kinda formal)
आप हैं = You are (plural/formal)
हम हैं = We are
वह/यह है = He/she is
वे/ये हैं = They are or He/She is (formal)
Basically, with the exception of मैं and तुम (which have the conjugations of हूँ and हो respectively), if the pronoun is singular/informal, use है. If the pronoun is plural/formal, use हैं.
Your list is good but it's missing singular formal for the 2nd person (you). What is the conjugation when you are using आप to refer to a single person? Is it still हैं or does it become है ?
आप is grammatically plural so it should be हैं. My Hindi book says that sometimes colloquially you will hear people mix forms using आप है or women using masculine verb endings but this is not proper and should be avoided.